Problem: Simplify the following expression: $x = \dfrac{-6t + 4}{3t + 5} - \dfrac{-10t + 9}{3t + 5}$
Since the expressions have the same denominator we simply subtract the numerators: $x = \dfrac{-6t + 4 - (-10t + 9)}{3t + 5}$ Distribute the negative sign: $x = \dfrac{-6t + 4 + 10t - 9}{3t + 5}$ Combine like terms: $x = \dfrac{4t - 5}{3t + 5}$